On the Degree Growth of Birational Mappings in Higher Dimension

الأصل · EN

Let f be a birational map of Cᵈ, and consider the degree complexity, or asymptotic degree growth rate δ(f)=ₙ→∞(deg(fⁿ))¹/ⁿ. We introduce a family of elementary maps, which have the form f=L∘ J, where L is (invertible) linear, and J(x₁,...,xd)=(x₁⁻¹,...,xd⁻¹). We develop a method of regularization and show how it can be used to compute δ for an elementary map.